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Undecidable First-Order Theories of Affine Geometries

Antti Kuusisto ; Jeremy Meyers ; Jonni Virtema.

Tarski initiated a logic-based approach to formal geometry that studies first-order structures with a ternary betweenness relation \beta, and a quaternary equidistance relation \equiv. Tarski established, inter alia, that the first-order (FO) theory of (R^2,\beta,\equiv) is decidable. Aiello and van&nbsp;[&hellip;]

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Rewritability in Monadic Disjunctive Datalog, MMSNP, and Expressive Description Logics

Cristina Feier ; Antti Kuusisto ; Carsten Lutz.

We study rewritability of monadic disjunctive Datalog programs, (the complements of) MMSNP sentences, and ontology-mediated queries (OMQs) based on expressive description logics of the ALC family and on conjunctive queries. We show that rewritability into FO and into monadic Datalog (MDLog) are&nbsp;[&hellip;]

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